Wave after wave of migrants have been rescued from rubber dinghies and rickety fishing boats in the Mediterranean over the last three days, with thousands ferried to Italy's southern shores.

Italian officials struggled Monday to find room in shelters in Sicily and the mainland for the nearly 6,800 refugees they said had been rescued at sea off the coast of Libya. The Italian navy said a woman, in labor when she was rescued Sunday, gave birth to a daughter on one of its patrol ships.

"You have to understand that Southern Europe is very much under pressure, not only from Libya, but even from Turkey," said Carlotta Sami, a spokeswoman for the U.N. High Commission for Refugees in Southern Europe. "The routes of refugees are increasingly bringing people towards Southern Europe, because there is very strong pressure of many conflicts, both in the Middle East and in many African countries."

Authorities said at least 10 migrants drowned in the last few days as they attempted to escape chaotic Libya for a more stable life in Europe.

The migrants arriving in southern Italy are being dispersed to reception centers across the country. Humanitarian aid workers say that many of them have legitimate claims to asylum in Europe as they are fleeing conflict and repression in such countries as Syria and Eritrea.

But not everyone in Europe is welcoming them.

The Milan-based governor of Lombardy, Roberto Maroni, said his region "has already done its part" and that any government funding "should be spent on our citizens and not for clandestine" migrants.

Some humanitarian aid groups have for called a country-by-country European Union quota to accept the migrants as they arrive on the continent's shores. But Czech Prime Minister Bohuslav Sobotka rejected that idea.

"The Czech Republic is not supporting the introduction of a obligatory quota, but in support of European solidarity we will decide about hosting migrants in our country depending on our situation and capacity," the Czech leader said. "So we clearly say 'no' to a quota, but 'yes' to solidarity with migrants."

Italy says mild weather and a calm Mediterranean are expected to push the number of migrant arrivals to 200,000 this year - 30,000 more than in 2014.

The unrelenting flood of migrants is continuing even after about 800 on one overcrowded boat drowned in a capsize last month. The captain of that boat mistakenly rammed it into a commercial ship on its way for a rescue operation.

Following a series of shipwrecks that killed more than 1,200 people in April, European leaders at an April 23 summit agreed to strengthen the EU presence at sea, deciding to triple the previous $3.4 million-a-month funding for the operation run by its Frontex border agency.